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quadrilateralcowboy/idlib/geometry/TraceModel.cpp
brendon 47a1010d23 Initial commit
2020-06-12 14:06:25 -07:00

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/*
===========================================================================
Doom 3 GPL Source Code
Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 GPL Source Code (?Doom 3 Source Code?).
Doom 3 Source Code is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Doom 3 Source Code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Doom 3 Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 Source Code. If not, please request a copy in writing from id Software at the address below.
If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.
===========================================================================
*/
#include "../../idlib/precompiled.h"
#pragma hdrstop
#include "TraceModel.h"
/*
============
idTraceModel::SetupBox
============
*/
void idTraceModel::SetupBox( const idBounds &boxBounds ) {
int i;
if ( type != TRM_BOX ) {
InitBox();
}
// offset to center
offset = ( boxBounds[0] + boxBounds[1] ) * 0.5f;
// set box vertices
for ( i = 0; i < 8; i++ ) {
verts[i][0] = boxBounds[(i^(i>>1))&1][0];
verts[i][1] = boxBounds[(i>>1)&1][1];
verts[i][2] = boxBounds[(i>>2)&1][2];
}
// set polygon plane distances
polys[0].dist = -boxBounds[0][2];
polys[1].dist = boxBounds[1][2];
polys[2].dist = -boxBounds[0][1];
polys[3].dist = boxBounds[1][0];
polys[4].dist = boxBounds[1][1];
polys[5].dist = -boxBounds[0][0];
// set polygon bounds
for ( i = 0; i < 6; i++ ) {
polys[i].bounds = boxBounds;
}
polys[0].bounds[1][2] = boxBounds[0][2];
polys[1].bounds[0][2] = boxBounds[1][2];
polys[2].bounds[1][1] = boxBounds[0][1];
polys[3].bounds[0][0] = boxBounds[1][0];
polys[4].bounds[0][1] = boxBounds[1][1];
polys[5].bounds[1][0] = boxBounds[0][0];
bounds = boxBounds;
}
/*
============
idTraceModel::SetupBox
The origin is placed at the center of the cube.
============
*/
void idTraceModel::SetupBox( const float size ) {
idBounds boxBounds;
float halfSize;
halfSize = size * 0.5f;
boxBounds[0].Set( -halfSize, -halfSize, -halfSize );
boxBounds[1].Set( halfSize, halfSize, halfSize );
SetupBox( boxBounds );
}
/*
============
idTraceModel::InitBox
Initialize size independent box.
============
*/
void idTraceModel::InitBox( void ) {
int i;
type = TRM_BOX;
numVerts = 8;
numEdges = 12;
numPolys = 6;
// set box edges
for ( i = 0; i < 4; i++ ) {
edges[ i + 1 ].v[0] = i;
edges[ i + 1 ].v[1] = (i + 1) & 3;
edges[ i + 5 ].v[0] = 4 + i;
edges[ i + 5 ].v[1] = 4 + ((i + 1) & 3);
edges[ i + 9 ].v[0] = i;
edges[ i + 9 ].v[1] = 4 + i;
}
// all edges of a polygon go counter clockwise
polys[0].numEdges = 4;
polys[0].edges[0] = -4;
polys[0].edges[1] = -3;
polys[0].edges[2] = -2;
polys[0].edges[3] = -1;
polys[0].normal.Set( 0.0f, 0.0f, -1.0f );
polys[1].numEdges = 4;
polys[1].edges[0] = 5;
polys[1].edges[1] = 6;
polys[1].edges[2] = 7;
polys[1].edges[3] = 8;
polys[1].normal.Set( 0.0f, 0.0f, 1.0f );
polys[2].numEdges = 4;
polys[2].edges[0] = 1;
polys[2].edges[1] = 10;
polys[2].edges[2] = -5;
polys[2].edges[3] = -9;
polys[2].normal.Set( 0.0f, -1.0f, 0.0f );
polys[3].numEdges = 4;
polys[3].edges[0] = 2;
polys[3].edges[1] = 11;
polys[3].edges[2] = -6;
polys[3].edges[3] = -10;
polys[3].normal.Set( 1.0f, 0.0f, 0.0f );
polys[4].numEdges = 4;
polys[4].edges[0] = 3;
polys[4].edges[1] = 12;
polys[4].edges[2] = -7;
polys[4].edges[3] = -11;
polys[4].normal.Set( 0.0f, 1.0f, 0.0f );
polys[5].numEdges = 4;
polys[5].edges[0] = 4;
polys[5].edges[1] = 9;
polys[5].edges[2] = -8;
polys[5].edges[3] = -12;
polys[5].normal.Set( -1.0f, 0.0f, 0.0f );
// convex model
isConvex = true;
GenerateEdgeNormals();
}
/*
============
idTraceModel::SetupOctahedron
============
*/
void idTraceModel::SetupOctahedron( const idBounds &octBounds ) {
int i, e0, e1, v0, v1, v2;
idVec3 v;
if ( type != TRM_OCTAHEDRON ) {
InitOctahedron();
}
offset = ( octBounds[0] + octBounds[1] ) * 0.5f;
v[0] = octBounds[1][0] - offset[0];
v[1] = octBounds[1][1] - offset[1];
v[2] = octBounds[1][2] - offset[2];
// set vertices
verts[0].Set( offset.x + v[0], offset.y, offset.z );
verts[1].Set( offset.x - v[0], offset.y, offset.z );
verts[2].Set( offset.x, offset.y + v[1], offset.z );
verts[3].Set( offset.x, offset.y - v[1], offset.z );
verts[4].Set( offset.x, offset.y, offset.z + v[2] );
verts[5].Set( offset.x, offset.y, offset.z - v[2] );
// set polygons
for ( i = 0; i < numPolys; i++ ) {
e0 = polys[i].edges[0];
e1 = polys[i].edges[1];
v0 = edges[abs(e0)].v[INTSIGNBITSET(e0)];
v1 = edges[abs(e0)].v[INTSIGNBITNOTSET(e0)];
v2 = edges[abs(e1)].v[INTSIGNBITNOTSET(e1)];
// polygon plane
polys[i].normal = ( verts[v1] - verts[v0] ).Cross( verts[v2] - verts[v0] );
polys[i].normal.Normalize();
polys[i].dist = polys[i].normal * verts[v0];
// polygon bounds
polys[i].bounds[0] = polys[i].bounds[1] = verts[v0];
polys[i].bounds.AddPoint( verts[v1] );
polys[i].bounds.AddPoint( verts[v2] );
}
// trm bounds
bounds = octBounds;
GenerateEdgeNormals();
}
/*
============
idTraceModel::SetupOctahedron
The origin is placed at the center of the octahedron.
============
*/
void idTraceModel::SetupOctahedron( const float size ) {
idBounds octBounds;
float halfSize;
halfSize = size * 0.5f;
octBounds[0].Set( -halfSize, -halfSize, -halfSize );
octBounds[1].Set( halfSize, halfSize, halfSize );
SetupOctahedron( octBounds );
}
/*
============
idTraceModel::InitOctahedron
Initialize size independent octahedron.
============
*/
void idTraceModel::InitOctahedron( void ) {
type = TRM_OCTAHEDRON;
numVerts = 6;
numEdges = 12;
numPolys = 8;
// set edges
edges[ 1].v[0] = 4; edges[ 1].v[1] = 0;
edges[ 2].v[0] = 0; edges[ 2].v[1] = 2;
edges[ 3].v[0] = 2; edges[ 3].v[1] = 4;
edges[ 4].v[0] = 2; edges[ 4].v[1] = 1;
edges[ 5].v[0] = 1; edges[ 5].v[1] = 4;
edges[ 6].v[0] = 1; edges[ 6].v[1] = 3;
edges[ 7].v[0] = 3; edges[ 7].v[1] = 4;
edges[ 8].v[0] = 3; edges[ 8].v[1] = 0;
edges[ 9].v[0] = 5; edges[ 9].v[1] = 2;
edges[10].v[0] = 0; edges[10].v[1] = 5;
edges[11].v[0] = 5; edges[11].v[1] = 1;
edges[12].v[0] = 5; edges[12].v[1] = 3;
// all edges of a polygon go counter clockwise
polys[0].numEdges = 3;
polys[0].edges[0] = 1;
polys[0].edges[1] = 2;
polys[0].edges[2] = 3;
polys[1].numEdges = 3;
polys[1].edges[0] = -3;
polys[1].edges[1] = 4;
polys[1].edges[2] = 5;
polys[2].numEdges = 3;
polys[2].edges[0] = -5;
polys[2].edges[1] = 6;
polys[2].edges[2] = 7;
polys[3].numEdges = 3;
polys[3].edges[0] = -7;
polys[3].edges[1] = 8;
polys[3].edges[2] = -1;
polys[4].numEdges = 3;
polys[4].edges[0] = 9;
polys[4].edges[1] = -2;
polys[4].edges[2] = 10;
polys[5].numEdges = 3;
polys[5].edges[0] = 11;
polys[5].edges[1] = -4;
polys[5].edges[2] = -9;
polys[6].numEdges = 3;
polys[6].edges[0] = 12;
polys[6].edges[1] = -6;
polys[6].edges[2] = -11;
polys[7].numEdges = 3;
polys[7].edges[0] = -10;
polys[7].edges[1] = -8;
polys[7].edges[2] = -12;
// convex model
isConvex = true;
}
/*
============
idTraceModel::SetupDodecahedron
============
*/
void idTraceModel::SetupDodecahedron( const idBounds &dodBounds ) {
int i, e0, e1, e2, e3, v0, v1, v2, v3, v4;
float s, d;
idVec3 a, b, c;
if ( type != TRM_DODECAHEDRON ) {
InitDodecahedron();
}
a[0] = a[1] = a[2] = 0.5773502691896257f; // 1.0f / ( 3.0f ) ^ 0.5f;
b[0] = b[1] = b[2] = 0.3568220897730899f; // ( ( 3.0f - ( 5.0f ) ^ 0.5f ) / 6.0f ) ^ 0.5f;
c[0] = c[1] = c[2] = 0.9341723589627156f; // ( ( 3.0f + ( 5.0f ) ^ 0.5f ) / 6.0f ) ^ 0.5f;
d = 0.5f / c[0];
s = ( dodBounds[1][0] - dodBounds[0][0] ) * d;
a[0] *= s;
b[0] *= s;
c[0] *= s;
s = ( dodBounds[1][1] - dodBounds[0][1] ) * d;
a[1] *= s;
b[1] *= s;
c[1] *= s;
s = ( dodBounds[1][2] - dodBounds[0][2] ) * d;
a[2] *= s;
b[2] *= s;
c[2] *= s;
offset = ( dodBounds[0] + dodBounds[1] ) * 0.5f;
// set vertices
verts[ 0].Set( offset.x + a[0], offset.y + a[1], offset.z + a[2] );
verts[ 1].Set( offset.x + a[0], offset.y + a[1], offset.z - a[2] );
verts[ 2].Set( offset.x + a[0], offset.y - a[1], offset.z + a[2] );
verts[ 3].Set( offset.x + a[0], offset.y - a[1], offset.z - a[2] );
verts[ 4].Set( offset.x - a[0], offset.y + a[1], offset.z + a[2] );
verts[ 5].Set( offset.x - a[0], offset.y + a[1], offset.z - a[2] );
verts[ 6].Set( offset.x - a[0], offset.y - a[1], offset.z + a[2] );
verts[ 7].Set( offset.x - a[0], offset.y - a[1], offset.z - a[2] );
verts[ 8].Set( offset.x + b[0], offset.y + c[1], offset.z );
verts[ 9].Set( offset.x - b[0], offset.y + c[1], offset.z );
verts[10].Set( offset.x + b[0], offset.y - c[1], offset.z );
verts[11].Set( offset.x - b[0], offset.y - c[1], offset.z );
verts[12].Set( offset.x + c[0], offset.y , offset.z + b[2] );
verts[13].Set( offset.x + c[0], offset.y , offset.z - b[2] );
verts[14].Set( offset.x - c[0], offset.y , offset.z + b[2] );
verts[15].Set( offset.x - c[0], offset.y , offset.z - b[2] );
verts[16].Set( offset.x , offset.y + b[1], offset.z + c[2] );
verts[17].Set( offset.x , offset.y - b[1], offset.z + c[2] );
verts[18].Set( offset.x , offset.y + b[1], offset.z - c[2] );
verts[19].Set( offset.x , offset.y - b[1], offset.z - c[2] );
// set polygons
for ( i = 0; i < numPolys; i++ ) {
e0 = polys[i].edges[0];
e1 = polys[i].edges[1];
e2 = polys[i].edges[2];
e3 = polys[i].edges[3];
v0 = edges[abs(e0)].v[INTSIGNBITSET(e0)];
v1 = edges[abs(e0)].v[INTSIGNBITNOTSET(e0)];
v2 = edges[abs(e1)].v[INTSIGNBITNOTSET(e1)];
v3 = edges[abs(e2)].v[INTSIGNBITNOTSET(e2)];
v4 = edges[abs(e3)].v[INTSIGNBITNOTSET(e3)];
// polygon plane
polys[i].normal = ( verts[v1] - verts[v0] ).Cross( verts[v2] - verts[v0] );
polys[i].normal.Normalize();
polys[i].dist = polys[i].normal * verts[v0];
// polygon bounds
polys[i].bounds[0] = polys[i].bounds[1] = verts[v0];
polys[i].bounds.AddPoint( verts[v1] );
polys[i].bounds.AddPoint( verts[v2] );
polys[i].bounds.AddPoint( verts[v3] );
polys[i].bounds.AddPoint( verts[v4] );
}
// trm bounds
bounds = dodBounds;
GenerateEdgeNormals();
}
/*
============
idTraceModel::SetupDodecahedron
The origin is placed at the center of the octahedron.
============
*/
void idTraceModel::SetupDodecahedron( const float size ) {
idBounds dodBounds;
float halfSize;
halfSize = size * 0.5f;
dodBounds[0].Set( -halfSize, -halfSize, -halfSize );
dodBounds[1].Set( halfSize, halfSize, halfSize );
SetupDodecahedron( dodBounds );
}
/*
============
idTraceModel::InitDodecahedron
Initialize size independent dodecahedron.
============
*/
void idTraceModel::InitDodecahedron( void ) {
type = TRM_DODECAHEDRON;
numVerts = 20;
numEdges = 30;
numPolys = 12;
// set edges
edges[ 1].v[0] = 0; edges[ 1].v[1] = 8;
edges[ 2].v[0] = 8; edges[ 2].v[1] = 9;
edges[ 3].v[0] = 9; edges[ 3].v[1] = 4;
edges[ 4].v[0] = 4; edges[ 4].v[1] = 16;
edges[ 5].v[0] = 16; edges[ 5].v[1] = 0;
edges[ 6].v[0] = 16; edges[ 6].v[1] = 17;
edges[ 7].v[0] = 17; edges[ 7].v[1] = 2;
edges[ 8].v[0] = 2; edges[ 8].v[1] = 12;
edges[ 9].v[0] = 12; edges[ 9].v[1] = 0;
edges[10].v[0] = 2; edges[10].v[1] = 10;
edges[11].v[0] = 10; edges[11].v[1] = 3;
edges[12].v[0] = 3; edges[12].v[1] = 13;
edges[13].v[0] = 13; edges[13].v[1] = 12;
edges[14].v[0] = 9; edges[14].v[1] = 5;
edges[15].v[0] = 5; edges[15].v[1] = 15;
edges[16].v[0] = 15; edges[16].v[1] = 14;
edges[17].v[0] = 14; edges[17].v[1] = 4;
edges[18].v[0] = 3; edges[18].v[1] = 19;
edges[19].v[0] = 19; edges[19].v[1] = 18;
edges[20].v[0] = 18; edges[20].v[1] = 1;
edges[21].v[0] = 1; edges[21].v[1] = 13;
edges[22].v[0] = 7; edges[22].v[1] = 11;
edges[23].v[0] = 11; edges[23].v[1] = 6;
edges[24].v[0] = 6; edges[24].v[1] = 14;
edges[25].v[0] = 15; edges[25].v[1] = 7;
edges[26].v[0] = 1; edges[26].v[1] = 8;
edges[27].v[0] = 18; edges[27].v[1] = 5;
edges[28].v[0] = 6; edges[28].v[1] = 17;
edges[29].v[0] = 11; edges[29].v[1] = 10;
edges[30].v[0] = 19; edges[30].v[1] = 7;
// all edges of a polygon go counter clockwise
polys[0].numEdges = 5;
polys[0].edges[0] = 1;
polys[0].edges[1] = 2;
polys[0].edges[2] = 3;
polys[0].edges[3] = 4;
polys[0].edges[4] = 5;
polys[1].numEdges = 5;
polys[1].edges[0] = -5;
polys[1].edges[1] = 6;
polys[1].edges[2] = 7;
polys[1].edges[3] = 8;
polys[1].edges[4] = 9;
polys[2].numEdges = 5;
polys[2].edges[0] = -8;
polys[2].edges[1] = 10;
polys[2].edges[2] = 11;
polys[2].edges[3] = 12;
polys[2].edges[4] = 13;
polys[3].numEdges = 5;
polys[3].edges[0] = 14;
polys[3].edges[1] = 15;
polys[3].edges[2] = 16;
polys[3].edges[3] = 17;
polys[3].edges[4] = -3;
polys[4].numEdges = 5;
polys[4].edges[0] = 18;
polys[4].edges[1] = 19;
polys[4].edges[2] = 20;
polys[4].edges[3] = 21;
polys[4].edges[4] = -12;
polys[5].numEdges = 5;
polys[5].edges[0] = 22;
polys[5].edges[1] = 23;
polys[5].edges[2] = 24;
polys[5].edges[3] = -16;
polys[5].edges[4] = 25;
polys[6].numEdges = 5;
polys[6].edges[0] = -9;
polys[6].edges[1] = -13;
polys[6].edges[2] = -21;
polys[6].edges[3] = 26;
polys[6].edges[4] = -1;
polys[7].numEdges = 5;
polys[7].edges[0] = -26;
polys[7].edges[1] = -20;
polys[7].edges[2] = 27;
polys[7].edges[3] = -14;
polys[7].edges[4] = -2;
polys[8].numEdges = 5;
polys[8].edges[0] = -4;
polys[8].edges[1] = -17;
polys[8].edges[2] = -24;
polys[8].edges[3] = 28;
polys[8].edges[4] = -6;
polys[9].numEdges = 5;
polys[9].edges[0] = -23;
polys[9].edges[1] = 29;
polys[9].edges[2] = -10;
polys[9].edges[3] = -7;
polys[9].edges[4] = -28;
polys[10].numEdges = 5;
polys[10].edges[0] = -25;
polys[10].edges[1] = -15;
polys[10].edges[2] = -27;
polys[10].edges[3] = -19;
polys[10].edges[4] = 30;
polys[11].numEdges = 5;
polys[11].edges[0] = -30;
polys[11].edges[1] = -18;
polys[11].edges[2] = -11;
polys[11].edges[3] = -29;
polys[11].edges[4] = -22;
// convex model
isConvex = true;
}
/*
============
idTraceModel::SetupCylinder
============
*/
void idTraceModel::SetupCylinder( const idBounds &cylBounds, const int numSides ) {
int i, n, ii, n2;
float angle;
idVec3 halfSize;
n = numSides;
if ( n < 3 ) {
n = 3;
}
if ( n * 2 > MAX_TRACEMODEL_VERTS ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many vertices\n" );
n = MAX_TRACEMODEL_VERTS / 2;
}
if ( n * 3 > MAX_TRACEMODEL_EDGES ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many sides\n" );
n = MAX_TRACEMODEL_EDGES / 3;
}
if ( n + 2 > MAX_TRACEMODEL_POLYS ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many polygons\n" );
n = MAX_TRACEMODEL_POLYS - 2;
}
type = TRM_CYLINDER;
numVerts = n * 2;
numEdges = n * 3;
numPolys = n + 2;
offset = ( cylBounds[0] + cylBounds[1] ) * 0.5f;
halfSize = cylBounds[1] - offset;
for ( i = 0; i < n; i++ ) {
// verts
angle = idMath::TWO_PI * i / n;
verts[i].x = cos( angle ) * halfSize.x + offset.x;
verts[i].y = sin( angle ) * halfSize.y + offset.y;
verts[i].z = -halfSize.z + offset.z;
verts[n+i].x = verts[i].x;
verts[n+i].y = verts[i].y;
verts[n+i].z = halfSize.z + offset.z;
// edges
ii = i + 1;
n2 = n << 1;
edges[ii].v[0] = i;
edges[ii].v[1] = ii % n;
edges[n+ii].v[0] = edges[ii].v[0] + n;
edges[n+ii].v[1] = edges[ii].v[1] + n;
edges[n2+ii].v[0] = i;
edges[n2+ii].v[1] = n + i;
// vertical polygon edges
polys[i].numEdges = 4;
polys[i].edges[0] = ii;
polys[i].edges[1] = n2 + (ii % n) + 1;
polys[i].edges[2] = -(n + ii);
polys[i].edges[3] = -(n2 + ii);
// bottom and top polygon edges
polys[n].edges[i] = -(n - i);
polys[n+1].edges[i] = n + ii;
}
// bottom and top polygon numEdges
polys[n].numEdges = n;
polys[n+1].numEdges = n;
// polygons
for ( i = 0; i < n; i++ ) {
// vertical polygon plane
polys[i].normal = (verts[(i+1)%n] - verts[i]).Cross( verts[n+i] - verts[i] );
polys[i].normal.Normalize();
polys[i].dist = polys[i].normal * verts[i];
// vertical polygon bounds
polys[i].bounds.Clear();
polys[i].bounds.AddPoint( verts[i] );
polys[i].bounds.AddPoint( verts[(i+1)%n] );
polys[i].bounds[0][2] = -halfSize.z + offset.z;
polys[i].bounds[1][2] = halfSize.z + offset.z;
}
// bottom and top polygon plane
polys[n].normal.Set( 0.0f, 0.0f, -1.0f );
polys[n].dist = -cylBounds[0][2];
polys[n+1].normal.Set( 0.0f, 0.0f, 1.0f );
polys[n+1].dist = cylBounds[1][2];
// trm bounds
bounds = cylBounds;
// bottom and top polygon bounds
polys[n].bounds = bounds;
polys[n].bounds[1][2] = bounds[0][2];
polys[n+1].bounds = bounds;
polys[n+1].bounds[0][2] = bounds[1][2];
// convex model
isConvex = true;
GenerateEdgeNormals();
}
/*
============
idTraceModel::SetupCylinder
The origin is placed at the center of the cylinder.
============
*/
void idTraceModel::SetupCylinder( const float height, const float width, const int numSides ) {
idBounds cylBounds;
float halfHeight, halfWidth;
halfHeight = height * 0.5f;
halfWidth = width * 0.5f;
cylBounds[0].Set( -halfWidth, -halfWidth, -halfHeight );
cylBounds[1].Set( halfWidth, halfWidth, halfHeight );
SetupCylinder( cylBounds, numSides );
}
/*
============
idTraceModel::SetupCone
============
*/
void idTraceModel::SetupCone( const idBounds &coneBounds, const int numSides ) {
int i, n, ii;
float angle;
idVec3 halfSize;
n = numSides;
if ( n < 2 ) {
n = 3;
}
if ( n + 1 > MAX_TRACEMODEL_VERTS ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many vertices\n" );
n = MAX_TRACEMODEL_VERTS - 1;
}
if ( n * 2 > MAX_TRACEMODEL_EDGES ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many edges\n" );
n = MAX_TRACEMODEL_EDGES / 2;
}
if ( n + 1 > MAX_TRACEMODEL_POLYS ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many polygons\n" );
n = MAX_TRACEMODEL_POLYS - 1;
}
type = TRM_CONE;
numVerts = n + 1;
numEdges = n * 2;
numPolys = n + 1;
offset = ( coneBounds[0] + coneBounds[1] ) * 0.5f;
halfSize = coneBounds[1] - offset;
verts[n].Set( 0.0f, 0.0f, halfSize.z + offset.z );
for ( i = 0; i < n; i++ ) {
// verts
angle = idMath::TWO_PI * i / n;
verts[i].x = cos( angle ) * halfSize.x + offset.x;
verts[i].y = sin( angle ) * halfSize.y + offset.y;
verts[i].z = -halfSize.z + offset.z;
// edges
ii = i + 1;
edges[ii].v[0] = i;
edges[ii].v[1] = ii % n;
edges[n+ii].v[0] = i;
edges[n+ii].v[1] = n;
// vertical polygon edges
polys[i].numEdges = 3;
polys[i].edges[0] = ii;
polys[i].edges[1] = n + (ii % n) + 1;
polys[i].edges[2] = -(n + ii);
// bottom polygon edges
polys[n].edges[i] = -(n - i);
}
// bottom polygon numEdges
polys[n].numEdges = n;
// polygons
for ( i = 0; i < n; i++ ) {
// polygon plane
polys[i].normal = (verts[(i+1)%n] - verts[i]).Cross( verts[n] - verts[i] );
polys[i].normal.Normalize();
polys[i].dist = polys[i].normal * verts[i];
// polygon bounds
polys[i].bounds.Clear();
polys[i].bounds.AddPoint( verts[i] );
polys[i].bounds.AddPoint( verts[(i+1)%n] );
polys[i].bounds.AddPoint( verts[n] );
}
// bottom polygon plane
polys[n].normal.Set( 0.0f, 0.0f, -1.0f );
polys[n].dist = -coneBounds[0][2];
// trm bounds
bounds = coneBounds;
// bottom polygon bounds
polys[n].bounds = bounds;
polys[n].bounds[1][2] = bounds[0][2];
// convex model
isConvex = true;
GenerateEdgeNormals();
}
/*
============
idTraceModel::SetupCone
The origin is placed at the apex of the cone.
============
*/
void idTraceModel::SetupCone( const float height, const float width, const int numSides ) {
idBounds coneBounds;
float halfWidth;
halfWidth = width * 0.5f;
coneBounds[0].Set( -halfWidth, -halfWidth, -height );
coneBounds[1].Set( halfWidth, halfWidth, 0.0f );
SetupCone( coneBounds, numSides );
}
/*
============
idTraceModel::SetupBone
The origin is placed at the center of the bone.
============
*/
void idTraceModel::SetupBone( const float length, const float width ) {
int i, j, edgeNum;
float halfLength = length * 0.5f;
if ( type != TRM_BONE ) {
InitBone();
}
// offset to center
offset.Set( 0.0f, 0.0f, 0.0f );
// set vertices
verts[0].Set( 0.0f, 0.0f, -halfLength );
verts[1].Set( 0.0f, width * -0.5f, 0.0f );
verts[2].Set( width * 0.5f, width * 0.25f, 0.0f );
verts[3].Set( width * -0.5f, width * 0.25f, 0.0f );
verts[4].Set( 0.0f, 0.0f, halfLength );
// set bounds
bounds[0].Set( width * -0.5f, width * -0.5f, -halfLength );
bounds[1].Set( width * 0.5f, width * 0.25f, halfLength );
// poly plane normals
polys[0].normal = ( verts[2] - verts[0] ).Cross( verts[1] - verts[0] );
polys[0].normal.Normalize();
polys[2].normal.Set( -polys[0].normal[0], polys[0].normal[1], polys[0].normal[2] );
polys[3].normal.Set( polys[0].normal[0], polys[0].normal[1], -polys[0].normal[2] );
polys[5].normal.Set( -polys[0].normal[0], polys[0].normal[1], -polys[0].normal[2] );
polys[1].normal = (verts[3] - verts[0]).Cross(verts[2] - verts[0]);
polys[1].normal.Normalize();
polys[4].normal.Set( polys[1].normal[0], polys[1].normal[1], -polys[1].normal[2] );
// poly plane distances
for ( i = 0; i < 6; i++ ) {
polys[i].dist = polys[i].normal * verts[ edges[ abs(polys[i].edges[0]) ].v[0] ];
polys[i].bounds.Clear();
for ( j = 0; j < 3; j++ ) {
edgeNum = polys[i].edges[ j ];
polys[i].bounds.AddPoint( verts[ edges[abs(edgeNum)].v[edgeNum < 0] ] );
}
}
GenerateEdgeNormals();
}
/*
============
idTraceModel::InitBone
Initialize size independent bone.
============
*/
void idTraceModel::InitBone( void ) {
int i;
type = TRM_BONE;
numVerts = 5;
numEdges = 9;
numPolys = 6;
// set bone edges
for ( i = 0; i < 3; i++ ) {
edges[ i + 1 ].v[0] = 0;
edges[ i + 1 ].v[1] = i + 1;
edges[ i + 4 ].v[0] = 1 + i;
edges[ i + 4 ].v[1] = 1 + ((i + 1) % 3);
edges[ i + 7 ].v[0] = i + 1;
edges[ i + 7 ].v[1] = 4;
}
// all edges of a polygon go counter clockwise
polys[0].numEdges = 3;
polys[0].edges[0] = 2;
polys[0].edges[1] = -4;
polys[0].edges[2] = -1;
polys[1].numEdges = 3;
polys[1].edges[0] = 3;
polys[1].edges[1] = -5;
polys[1].edges[2] = -2;
polys[2].numEdges = 3;
polys[2].edges[0] = 1;
polys[2].edges[1] = -6;
polys[2].edges[2] = -3;
polys[3].numEdges = 3;
polys[3].edges[0] = 4;
polys[3].edges[1] = 8;
polys[3].edges[2] = -7;
polys[4].numEdges = 3;
polys[4].edges[0] = 5;
polys[4].edges[1] = 9;
polys[4].edges[2] = -8;
polys[5].numEdges = 3;
polys[5].edges[0] = 6;
polys[5].edges[1] = 7;
polys[5].edges[2] = -9;
// convex model
isConvex = true;
}
/*
============
idTraceModel::SetupPolygon
============
*/
void idTraceModel::SetupPolygon( const idVec3 *v, const int count ) {
int i, j;
idVec3 mid;
type = TRM_POLYGON;
numVerts = count;
// times three because we need to be able to turn the polygon into a volume
if ( numVerts * 3 > MAX_TRACEMODEL_EDGES ) {
idLib::common->Printf( "WARNING: idTraceModel::SetupPolygon: too many vertices\n" );
numVerts = MAX_TRACEMODEL_EDGES / 3;
}
numEdges = numVerts;
numPolys = 2;
// set polygon planes
polys[0].numEdges = numEdges;
polys[0].normal = ( v[1] - v[0] ).Cross( v[2] - v[0] );
polys[0].normal.Normalize();
polys[0].dist = polys[0].normal * v[0];
polys[1].numEdges = numEdges;
polys[1].normal = -polys[0].normal;
polys[1].dist = -polys[0].dist;
// setup verts, edges and polygons
polys[0].bounds.Clear();
mid = vec3_origin;
for ( i = 0, j = 1; i < numVerts; i++, j++ ) {
if ( j >= numVerts ) {
j = 0;
}
verts[i] = v[i];
edges[i+1].v[0] = i;
edges[i+1].v[1] = j;
edges[i+1].normal = polys[0].normal.Cross( v[i] - v[j] );
edges[i+1].normal.Normalize();
polys[0].edges[i] = i + 1;
polys[1].edges[i] = -(numVerts - i);
polys[0].bounds.AddPoint( verts[i] );
mid += v[i];
}
polys[1].bounds = polys[0].bounds;
// offset to center
offset = mid * (1.0f / numVerts);
// total bounds
bounds = polys[0].bounds;
// considered non convex because the model has no volume
isConvex = false;
}
/*
============
idTraceModel::SetupPolygon
============
*/
void idTraceModel::SetupPolygon( const idWinding &w ) {
int i;
idVec3 *verts;
verts = (idVec3 *) _alloca16( w.GetNumPoints() * sizeof( idVec3 ) );
for ( i = 0; i < w.GetNumPoints(); i++ ) {
verts[i] = w[i].ToVec3();
}
SetupPolygon( verts, w.GetNumPoints() );
}
/*
============
idTraceModel::VolumeFromPolygon
============
*/
void idTraceModel::VolumeFromPolygon( idTraceModel &trm, float thickness ) const {
int i;
trm = *this;
trm.type = TRM_POLYGONVOLUME;
trm.numVerts = numVerts * 2;
trm.numEdges = numEdges * 3;
trm.numPolys = numEdges + 2;
for ( i = 0; i < numEdges; i++ ) {
trm.verts[ numVerts + i ] = verts[i] - thickness * polys[0].normal;
trm.edges[ numEdges + i + 1 ].v[0] = numVerts + i;
trm.edges[ numEdges + i + 1 ].v[1] = numVerts + (i+1) % numVerts;
trm.edges[ numEdges * 2 + i + 1 ].v[0] = i;
trm.edges[ numEdges * 2 + i + 1 ].v[1] = numVerts + i;
trm.polys[1].edges[i] = -(numEdges + i + 1);
trm.polys[2+i].numEdges = 4;
trm.polys[2+i].edges[0] = -(i + 1);
trm.polys[2+i].edges[1] = numEdges*2 + i + 1;
trm.polys[2+i].edges[2] = numEdges + i + 1;
trm.polys[2+i].edges[3] = -(numEdges*2 + (i+1) % numEdges + 1);
trm.polys[2+i].normal = (verts[(i + 1) % numVerts] - verts[i]).Cross( polys[0].normal );
trm.polys[2+i].normal.Normalize();
trm.polys[2+i].dist = trm.polys[2+i].normal * verts[i];
}
trm.polys[1].dist = trm.polys[1].normal * trm.verts[ numEdges ];
trm.GenerateEdgeNormals();
}
/*
============
idTraceModel::GenerateEdgeNormals
============
*/
#define SHARP_EDGE_DOT -0.7f
int idTraceModel::GenerateEdgeNormals( void ) {
int i, j, edgeNum, numSharpEdges;
float dot;
idVec3 dir;
traceModelPoly_t *poly;
traceModelEdge_t *edge;
for ( i = 0; i <= numEdges; i++ ) {
edges[i].normal.Zero();
}
numSharpEdges = 0;
for ( i = 0; i < numPolys; i++ ) {
poly = polys + i;
for ( j = 0; j < poly->numEdges; j++ ) {
edgeNum = poly->edges[j];
edge = edges + abs( edgeNum );
if ( edge->normal[0] == 0.0f && edge->normal[1] == 0.0f && edge->normal[2] == 0.0f ) {
edge->normal = poly->normal;
}
else {
dot = edge->normal * poly->normal;
// if the two planes make a very sharp edge
if ( dot < SHARP_EDGE_DOT ) {
// max length normal pointing outside both polygons
dir = verts[ edge->v[edgeNum > 0]] - verts[ edge->v[edgeNum < 0]];
edge->normal = edge->normal.Cross( dir ) + poly->normal.Cross( -dir );
edge->normal *= ( 0.5f / ( 0.5f + 0.5f * SHARP_EDGE_DOT ) ) / edge->normal.Length();
numSharpEdges++;
}
else {
edge->normal = ( 0.5f / ( 0.5f + 0.5f * dot ) ) * ( edge->normal + poly->normal );
}
}
}
}
return numSharpEdges;
}
/*
============
idTraceModel::Translate
============
*/
void idTraceModel::Translate( const idVec3 &translation ) {
int i;
for ( i = 0; i < numVerts; i++ ) {
verts[i] += translation;
}
for ( i = 0; i < numPolys; i++ ) {
polys[i].dist += polys[i].normal * translation;
polys[i].bounds[0] += translation;
polys[i].bounds[1] += translation;
}
offset += translation;
bounds[0] += translation;
bounds[1] += translation;
}
/*
============
idTraceModel::Rotate
============
*/
void idTraceModel::Rotate( const idMat3 &rotation ) {
int i, j, edgeNum;
for ( i = 0; i < numVerts; i++ ) {
verts[i] *= rotation;
}
bounds.Clear();
for ( i = 0; i < numPolys; i++ ) {
polys[i].normal *= rotation;
polys[i].bounds.Clear();
edgeNum = 0;
for ( j = 0; j < polys[i].numEdges; j++ ) {
edgeNum = polys[i].edges[j];
polys[i].bounds.AddPoint( verts[edges[abs(edgeNum)].v[INTSIGNBITSET(edgeNum)]] );
}
polys[i].dist = polys[i].normal * verts[edges[abs(edgeNum)].v[INTSIGNBITSET(edgeNum)]];
bounds += polys[i].bounds;
}
GenerateEdgeNormals();
}
/*
============
idTraceModel::Shrink
============
*/
void idTraceModel::Shrink( const float m ) {
int i, j, edgeNum;
traceModelEdge_t *edge;
idVec3 dir;
if ( type == TRM_POLYGON ) {
for ( i = 0; i < numEdges; i++ ) {
edgeNum = polys[0].edges[i];
edge = &edges[abs(edgeNum)];
dir = verts[ edge->v[ INTSIGNBITSET(edgeNum) ] ] - verts[ edge->v[ INTSIGNBITNOTSET(edgeNum) ] ];
if ( dir.Normalize() < 2.0f * m ) {
continue;
}
dir *= m;
verts[ edge->v[ 0 ] ] -= dir;
verts[ edge->v[ 1 ] ] += dir;
}
return;
}
for ( i = 0; i < numPolys; i++ ) {
polys[i].dist -= m;
for ( j = 0; j < polys[i].numEdges; j++ ) {
edgeNum = polys[i].edges[j];
edge = &edges[abs(edgeNum)];
verts[ edge->v[ INTSIGNBITSET(edgeNum) ] ] -= polys[i].normal * m;
}
}
}
/*
============
idTraceModel::Compare
============
*/
bool idTraceModel::Compare( const idTraceModel &trm ) const {
int i;
if ( type != trm.type || numVerts != trm.numVerts ||
numEdges != trm.numEdges || numPolys != trm.numPolys ) {
return false;
}
if ( bounds != trm.bounds || offset != trm.offset ) {
return false;
}
switch( type ) {
case TRM_INVALID:
case TRM_BOX:
case TRM_OCTAHEDRON:
case TRM_DODECAHEDRON:
case TRM_CYLINDER:
case TRM_CONE:
break;
case TRM_BONE:
case TRM_POLYGON:
case TRM_POLYGONVOLUME:
case TRM_CUSTOM:
for ( i = 0; i < trm.numVerts; i++ ) {
if ( verts[i] != trm.verts[i] ) {
return false;
}
}
break;
}
return true;
}
/*
============
idTraceModel::GetPolygonArea
============
*/
float idTraceModel::GetPolygonArea( int polyNum ) const {
int i;
idVec3 base, v1, v2, cross;
float total;
const traceModelPoly_t *poly;
if ( polyNum < 0 || polyNum >= numPolys ) {
return 0.0f;
}
poly = &polys[polyNum];
total = 0.0f;
base = verts[ edges[ abs(poly->edges[0]) ].v[ INTSIGNBITSET( poly->edges[0] ) ] ];
for ( i = 0; i < poly->numEdges; i++ ) {
v1 = verts[ edges[ abs(poly->edges[i]) ].v[ INTSIGNBITSET( poly->edges[i] ) ] ] - base;
v2 = verts[ edges[ abs(poly->edges[i]) ].v[ INTSIGNBITNOTSET( poly->edges[i] ) ] ] - base;
cross = v1.Cross( v2 );
total += cross.Length();
}
return total * 0.5f;
}
/*
============
idTraceModel::GetOrderedSilhouetteEdges
============
*/
int idTraceModel::GetOrderedSilhouetteEdges( const int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1], int silEdges[MAX_TRACEMODEL_EDGES] ) const {
int i, j, edgeNum, numSilEdges, nextSilVert;
int unsortedSilEdges[MAX_TRACEMODEL_EDGES];
numSilEdges = 0;
for ( i = 1; i <= numEdges; i++ ) {
if ( edgeIsSilEdge[i] ) {
unsortedSilEdges[numSilEdges++] = i;
}
}
silEdges[0] = unsortedSilEdges[0];
unsortedSilEdges[0] = -1;
nextSilVert = edges[silEdges[0]].v[0];
for ( i = 1; i < numSilEdges; i++ ) {
for ( j = 1; j < numSilEdges; j++ ) {
edgeNum = unsortedSilEdges[j];
if ( edgeNum >= 0 ) {
if ( edges[edgeNum].v[0] == nextSilVert ) {
nextSilVert = edges[edgeNum].v[1];
silEdges[i] = edgeNum;
break;
}
if ( edges[edgeNum].v[1] == nextSilVert ) {
nextSilVert = edges[edgeNum].v[0];
silEdges[i] = -edgeNum;
break;
}
}
}
if ( j >= numSilEdges ) {
silEdges[i] = 1; // shouldn't happen
}
unsortedSilEdges[j] = -1;
}
return numSilEdges;
}
/*
============
idTraceModel::GetProjectionSilhouetteEdges
============
*/
int idTraceModel::GetProjectionSilhouetteEdges( const idVec3 &projectionOrigin, int silEdges[MAX_TRACEMODEL_EDGES] ) const {
int i, j, edgeNum;
int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1];
const traceModelPoly_t *poly;
idVec3 dir;
memset( edgeIsSilEdge, 0, sizeof( edgeIsSilEdge ) );
for ( i = 0; i < numPolys; i++ ) {
poly = &polys[i];
edgeNum = poly->edges[0];
dir = verts[ edges[abs(edgeNum)].v[ INTSIGNBITSET(edgeNum) ] ] - projectionOrigin;
if ( dir * poly->normal < 0.0f ) {
for ( j = 0; j < poly->numEdges; j++ ) {
edgeNum = poly->edges[j];
edgeIsSilEdge[abs(edgeNum)] ^= 1;
}
}
}
return GetOrderedSilhouetteEdges( edgeIsSilEdge, silEdges );
}
/*
============
idTraceModel::GetParallelProjectionSilhouetteEdges
============
*/
int idTraceModel::GetParallelProjectionSilhouetteEdges( const idVec3 &projectionDir, int silEdges[MAX_TRACEMODEL_EDGES] ) const {
int i, j, edgeNum;
int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1];
const traceModelPoly_t *poly;
memset( edgeIsSilEdge, 0, sizeof( edgeIsSilEdge ) );
for ( i = 0; i < numPolys; i++ ) {
poly = &polys[i];
if ( projectionDir * poly->normal < 0.0f ) {
for ( j = 0; j < poly->numEdges; j++ ) {
edgeNum = poly->edges[j];
edgeIsSilEdge[abs(edgeNum)] ^= 1;
}
}
}
return GetOrderedSilhouetteEdges( edgeIsSilEdge, silEdges );
}
/*
credits to Brian Mirtich for his paper "Fast and Accurate Computation of Polyhedral Mass Properties"
*/
typedef struct projectionIntegrals_s {
float P1;
float Pa, Pb;
float Paa, Pab, Pbb;
float Paaa, Paab, Pabb, Pbbb;
} projectionIntegrals_t;
/*
============
idTraceModel::ProjectionIntegrals
============
*/
void idTraceModel::ProjectionIntegrals( int polyNum, int a, int b, struct projectionIntegrals_s &integrals ) const {
const traceModelPoly_t *poly;
int i, edgeNum;
idVec3 v1, v2;
float a0, a1, da;
float b0, b1, db;
float a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
float a1_2, a1_3, b1_2, b1_3;
float C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
float Cab, Kab, Caab, Kaab, Cabb, Kabb;
memset(&integrals, 0, sizeof(projectionIntegrals_t));
poly = &polys[polyNum];
for ( i = 0; i < poly->numEdges; i++ ) {
edgeNum = poly->edges[i];
v1 = verts[ edges[ abs(edgeNum) ].v[ edgeNum < 0 ] ];
v2 = verts[ edges[ abs(edgeNum) ].v[ edgeNum > 0 ] ];
a0 = v1[a];
b0 = v1[b];
a1 = v2[a];
b1 = v2[b];
da = a1 - a0;
db = b1 - b0;
a0_2 = a0 * a0;
a0_3 = a0_2 * a0;
a0_4 = a0_3 * a0;
b0_2 = b0 * b0;
b0_3 = b0_2 * b0;
b0_4 = b0_3 * b0;
a1_2 = a1 * a1;
a1_3 = a1_2 * a1;
b1_2 = b1 * b1;
b1_3 = b1_2 * b1;
C1 = a1 + a0;
Ca = a1 * C1 + a0_2;
Caa = a1 * Ca + a0_3;
Caaa = a1 * Caa + a0_4;
Cb = b1 * (b1 + b0) + b0_2;
Cbb = b1 * Cb + b0_3;
Cbbb = b1 * Cbb + b0_4;
Cab = 3 * a1_2 + 2 * a1 * a0 + a0_2;
Kab = a1_2 + 2 * a1 * a0 + 3 * a0_2;
Caab = a0 * Cab + 4 * a1_3;
Kaab = a1 * Kab + 4 * a0_3;
Cabb = 4 * b1_3 + 3 * b1_2 * b0 + 2 * b1 * b0_2 + b0_3;
Kabb = b1_3 + 2 * b1_2 * b0 + 3 * b1 * b0_2 + 4 * b0_3;
integrals.P1 += db * C1;
integrals.Pa += db * Ca;
integrals.Paa += db * Caa;
integrals.Paaa += db * Caaa;
integrals.Pb += da * Cb;
integrals.Pbb += da * Cbb;
integrals.Pbbb += da * Cbbb;
integrals.Pab += db * (b1 * Cab + b0 * Kab);
integrals.Paab += db * (b1 * Caab + b0 * Kaab);
integrals.Pabb += da * (a1 * Cabb + a0 * Kabb);
}
integrals.P1 *= (1.0f / 2.0f);
integrals.Pa *= (1.0f / 6.0f);
integrals.Paa *= (1.0f / 12.0f);
integrals.Paaa *= (1.0f / 20.0f);
integrals.Pb *= (1.0f / -6.0f);
integrals.Pbb *= (1.0f / -12.0f);
integrals.Pbbb *= (1.0f / -20.0f);
integrals.Pab *= (1.0f / 24.0f);
integrals.Paab *= (1.0f / 60.0f);
integrals.Pabb *= (1.0f / -60.0f);
}
typedef struct polygonIntegrals_s {
float Fa, Fb, Fc;
float Faa, Fbb, Fcc;
float Faaa, Fbbb, Fccc;
float Faab, Fbbc, Fcca;
} polygonIntegrals_t;
/*
============
idTraceModel::PolygonIntegrals
============
*/
void idTraceModel::PolygonIntegrals( int polyNum, int a, int b, int c, struct polygonIntegrals_s &integrals ) const {
projectionIntegrals_t pi;
idVec3 n;
float w;
float k1, k2, k3, k4;
ProjectionIntegrals( polyNum, a, b, pi );
n = polys[polyNum].normal;
w = -polys[polyNum].dist;
k1 = 1 / n[c];
k2 = k1 * k1;
k3 = k2 * k1;
k4 = k3 * k1;
integrals.Fa = k1 * pi.Pa;
integrals.Fb = k1 * pi.Pb;
integrals.Fc = -k2 * (n[a] * pi.Pa + n[b] * pi.Pb + w * pi.P1);
integrals.Faa = k1 * pi.Paa;
integrals.Fbb = k1 * pi.Pbb;
integrals.Fcc = k3 * (Square(n[a]) * pi.Paa + 2 * n[a] * n[b] * pi.Pab + Square(n[b]) * pi.Pbb
+ w * (2 * (n[a] * pi.Pa + n[b] * pi.Pb) + w * pi.P1));
integrals.Faaa = k1 * pi.Paaa;
integrals.Fbbb = k1 * pi.Pbbb;
integrals.Fccc = -k4 * (Cube(n[a]) * pi.Paaa + 3 * Square(n[a]) * n[b] * pi.Paab
+ 3 * n[a] * Square(n[b]) * pi.Pabb + Cube(n[b]) * pi.Pbbb
+ 3 * w * (Square(n[a]) * pi.Paa + 2 * n[a] * n[b] * pi.Pab + Square(n[b]) * pi.Pbb)
+ w * w * (3 * (n[a] * pi.Pa + n[b] * pi.Pb) + w * pi.P1));
integrals.Faab = k1 * pi.Paab;
integrals.Fbbc = -k2 * (n[a] * pi.Pabb + n[b] * pi.Pbbb + w * pi.Pbb);
integrals.Fcca = k3 * (Square(n[a]) * pi.Paaa + 2 * n[a] * n[b] * pi.Paab + Square(n[b]) * pi.Pabb
+ w * (2 * (n[a] * pi.Paa + n[b] * pi.Pab) + w * pi.Pa));
}
typedef struct volumeIntegrals_s {
float T0;
idVec3 T1;
idVec3 T2;
idVec3 TP;
} volumeIntegrals_t;
/*
============
idTraceModel::VolumeIntegrals
============
*/
void idTraceModel::VolumeIntegrals( struct volumeIntegrals_s &integrals ) const {
const traceModelPoly_t *poly;
polygonIntegrals_t pi;
int i, a, b, c;
float nx, ny, nz;
memset( &integrals, 0, sizeof(volumeIntegrals_t) );
for ( i = 0; i < numPolys; i++ ) {
poly = &polys[i];
nx = idMath::Fabs( poly->normal[0] );
ny = idMath::Fabs( poly->normal[1] );
nz = idMath::Fabs( poly->normal[2] );
if ( nx > ny && nx > nz ) {
c = 0;
}
else {
c = (ny > nz) ? 1 : 2;
}
a = (c + 1) % 3;
b = (a + 1) % 3;
PolygonIntegrals( i, a, b, c, pi );
integrals.T0 += poly->normal[0] * ((a == 0) ? pi.Fa : ((b == 0) ? pi.Fb : pi.Fc));
integrals.T1[a] += poly->normal[a] * pi.Faa;
integrals.T1[b] += poly->normal[b] * pi.Fbb;
integrals.T1[c] += poly->normal[c] * pi.Fcc;
integrals.T2[a] += poly->normal[a] * pi.Faaa;
integrals.T2[b] += poly->normal[b] * pi.Fbbb;
integrals.T2[c] += poly->normal[c] * pi.Fccc;
integrals.TP[a] += poly->normal[a] * pi.Faab;
integrals.TP[b] += poly->normal[b] * pi.Fbbc;
integrals.TP[c] += poly->normal[c] * pi.Fcca;
}
integrals.T1 *= 0.5f;
integrals.T2 *= (1.0f / 3.0f);
integrals.TP *= 0.5f;
}
/*
============
idTraceModel::GetMassProperties
============
*/
void idTraceModel::GetMassProperties( const float density, float &mass, idVec3 &centerOfMass, idMat3 &inertiaTensor ) const {
volumeIntegrals_t integrals;
// if polygon trace model
if ( type == TRM_POLYGON ) {
idTraceModel trm;
VolumeFromPolygon( trm, 1.0f );
trm.GetMassProperties( density, mass, centerOfMass, inertiaTensor );
return;
}
VolumeIntegrals( integrals );
// if no volume
if ( integrals.T0 == 0.0f ) {
mass = 1.0f;
centerOfMass.Zero();
inertiaTensor.Identity();
return;
}
// mass of model
mass = density * integrals.T0;
// center of mass
centerOfMass = integrals.T1 / integrals.T0;
// compute inertia tensor
inertiaTensor[0][0] = density * (integrals.T2[1] + integrals.T2[2]);
inertiaTensor[1][1] = density * (integrals.T2[2] + integrals.T2[0]);
inertiaTensor[2][2] = density * (integrals.T2[0] + integrals.T2[1]);
inertiaTensor[0][1] = inertiaTensor[1][0] = - density * integrals.TP[0];
inertiaTensor[1][2] = inertiaTensor[2][1] = - density * integrals.TP[1];
inertiaTensor[2][0] = inertiaTensor[0][2] = - density * integrals.TP[2];
// translate inertia tensor to center of mass
inertiaTensor[0][0] -= mass * (centerOfMass[1]*centerOfMass[1] + centerOfMass[2]*centerOfMass[2]);
inertiaTensor[1][1] -= mass * (centerOfMass[2]*centerOfMass[2] + centerOfMass[0]*centerOfMass[0]);
inertiaTensor[2][2] -= mass * (centerOfMass[0]*centerOfMass[0] + centerOfMass[1]*centerOfMass[1]);
inertiaTensor[0][1] = inertiaTensor[1][0] += mass * centerOfMass[0] * centerOfMass[1];
inertiaTensor[1][2] = inertiaTensor[2][1] += mass * centerOfMass[1] * centerOfMass[2];
inertiaTensor[2][0] = inertiaTensor[0][2] += mass * centerOfMass[2] * centerOfMass[0];
}
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